Symplectic finite-difference time-domain method for maxwell equations

We introduce a symplectic finite-difference time-domain method for electromagnetic field simulation. Our method can successfully solve Maxwell equations involving conductor loss, which cannot be solved by the symplectic integration methods that have been presented in previous works. A class of high-order symplectic schemes for computing the time-dependent electric and magnetic fields are derived on the basis of an s-stage symplectic partitioned Runge–Kutta method.We present numerical results to illustrate the validity and accuracy of the algorithm.

[1]  Yoshio Suzuki,et al.  The symplectic finite difference time domain method , 2001 .

[2]  N. Anderson,et al.  Helicity and variational principles for Maxwell's equations , 1983 .

[3]  W. Tabbara,et al.  A fourth order scheme for the FDTD algorithm applied to Maxwell's equations , 1992, IEEE Antennas and Propagation Society International Symposium 1992 Digest.

[4]  I. Saitoh,et al.  Stability of symplectic finite-difference time-domain methods , 2002 .

[5]  P. Rentrop,et al.  Multirate Partitioned Runge-Kutta Methods , 2001 .

[6]  G. Rodrigue,et al.  High-order symplectic integration methods for finite element solutions to time dependent Maxwell equations , 2004, IEEE Transactions on Antennas and Propagation.

[7]  Andrew F. Peterson,et al.  Relative accuracy of several finite-difference time-domain methods in two and three dimensions , 1993 .

[8]  C. Trowbridge,et al.  Some key developments in computational electromagnetics and their attribution , 2006, IEEE Transactions on Magnetics.

[9]  Geng.  CONSTRUCTION OF HIGH ORDER SYMPLECTIC PRK METHODS , 1995 .

[10]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[11]  J. M. Sanz-Serna,et al.  Numerical Hamiltonian Problems , 1994 .

[12]  H. Yoshida.  Construction of higher order symplectic integrators , 1990 .

[13]  Jin-Fa Lee,et al.  Solving electromagnetic problems using a novel symmetric FEM-BEM approach , 2006, IEEE Transactions on Magnetics.

[14]  M. Kusaf,et al.  Optimized exponential operator coefficients for symplectic FDTD method , 2005, IEEE Microwave and Wireless Components Letters.

[15]  Yajuan Sun,et al.  Quadratic invariants and multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs , 2007, Numerische Mathematik.

[16]  M. Suzuki,et al.  General theory of higher-order decomposition of exponential operators and symplectic integrators , 1992 .

[17]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[18]  T. Hirono,et al.  Stability and numerical dispersion of symplectic fourth-order time-domain schemes for optical field simulation , 1998 .

[19]  Peter G. Petropoulos,et al.  Phase error control for FD-TD methods of second and fourth order accuracy , 1994 .

[20]  T. Hirono,et al.  Time-domain simulation of electromagnetic field using a symplectic integrator , 1997 .